Impact of Imperfect Timekeeping on Quantum Control

Area of Science:

• Quantum Information Science
• Quantum Control Theory
• Quantum Thermodynamics

Background:

• Unitary evolution of quantum systems necessitates precise knowledge of time.
• Physical clocks inherently possess limitations in characterizing time perfectly.
• Controlled quantum operations are fundamental in quantum computation and thermodynamics.

Purpose of the Study:

• To investigate the impact of imperfect timekeeping on controlled quantum operations.
• To establish bounds on achievable performance in quantum computation and thermodynamics under timekeeping limitations.

Main Methods:

• Derivation of an upper bound on average gate fidelity for random circuits with imperfect timekeeping.
• Analysis of qubit cooling in quantum thermodynamics using timers of varying quality.
• Integration of techniques from autonomous quantum clocks and quantum channel theory.

Main Results:

• Timekeeping quality imposes a limit on the achievable circuit complexity in quantum computation.
• Imperfect timekeeping affects the rate of qubit cooling but not the final achievable temperature in quantum thermodynamics.

Conclusions:

• Limitations in timekeeping knowledge significantly influence quantum computational capabilities.
• Quantum thermodynamic processes, such as qubit cooling, are robust to timekeeping errors, with effects primarily on dynamics rather than steady states.